{"title":"A differentiable structural analysis framework for high-performance design optimization","authors":"Keith J. Lee, Yijiang Huang, Caitlin T. Mueller","doi":"arxiv-2409.09247","DOIUrl":null,"url":null,"abstract":"Fast, gradient-based structural optimization has long been limited to a\nhighly restricted subset of problems -- namely, density-based compliance\nminimization -- for which gradients can be analytically derived. For other\nobjective functions, constraints, and design parameterizations, computing\ngradients has remained inaccessible, requiring the use of derivative-free\nalgorithms that scale poorly with problem size. This has restricted the\napplicability of optimization to abstracted and academic problems, and has\nlimited the uptake of these potentially impactful methods in practice. In this\npaper, we bridge the gap between computational efficiency and the freedom of\nproblem formulation through a differentiable analysis framework designed for\ngeneral structural optimization. We achieve this through leveraging Automatic\nDifferentiation (AD) to manage the complex computational graph of structural\nanalysis programs, and implementing specific derivation rules for performance\ncritical functions along this graph. This paper provides a complete overview of\ngradient computation for arbitrary structural design objectives, identifies the\nbarriers to their practical use, and derives key intermediate derivative\noperations that resolves these bottlenecks. Our framework is then tested\nagainst a series of structural design problems of increasing complexity: two\nhighly constrained minimum volume problem, a multi-stage shape and section\ndesign problem, and an embodied carbon minimization problem. We benchmark our\nframework against other common optimization approaches, and show that our\nmethod outperforms others in terms of speed, stability, and solution quality.","PeriodicalId":501309,"journal":{"name":"arXiv - CS - Computational Engineering, Finance, and Science","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Computational Engineering, Finance, and Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09247","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Fast, gradient-based structural optimization has long been limited to a
highly restricted subset of problems -- namely, density-based compliance
minimization -- for which gradients can be analytically derived. For other
objective functions, constraints, and design parameterizations, computing
gradients has remained inaccessible, requiring the use of derivative-free
algorithms that scale poorly with problem size. This has restricted the
applicability of optimization to abstracted and academic problems, and has
limited the uptake of these potentially impactful methods in practice. In this
paper, we bridge the gap between computational efficiency and the freedom of
problem formulation through a differentiable analysis framework designed for
general structural optimization. We achieve this through leveraging Automatic
Differentiation (AD) to manage the complex computational graph of structural
analysis programs, and implementing specific derivation rules for performance
critical functions along this graph. This paper provides a complete overview of
gradient computation for arbitrary structural design objectives, identifies the
barriers to their practical use, and derives key intermediate derivative
operations that resolves these bottlenecks. Our framework is then tested
against a series of structural design problems of increasing complexity: two
highly constrained minimum volume problem, a multi-stage shape and section
design problem, and an embodied carbon minimization problem. We benchmark our
framework against other common optimization approaches, and show that our
method outperforms others in terms of speed, stability, and solution quality.